Your research statement is going to be read by a hiring committee that has nobody in your field, because if they did have someone in your field, they wouldn't need to hire you.
Your statement must therefore focus on the problems you have solved or are trying to solve, why those problems are important, and what impact the solutions will have. It can also sketch the shape of those solutions.
Your vita carries some of the weight, so your statement need not duplicate your vita—although if you have such merits as best papers, publications in top conference, and so on, it is good to mention this in a sentence.
A faculty search, particularly if it is "open", gets hundreds of applications. (The search that hired me got 700 applications.) Your research statement will therefore be read primarily by tired, grumpy people. So it should be clear, short, and compelling. Apply everything you know about writing.
(Don't get discouraged by the large numbers of applications. In addition to being a faculty candidate, I have also been on hiring committees when hundreds of applications were involved. The candidates who are obviously unsuitable are weeded out quickly. The candidates who make the short list
Take care of what you can—the first two—and chances are your application will also make the short list.)
From time to time I have heard a successful senior scientist say about one person or another, "That person needs to learn to sell himself." I have never found this sort of advice useful—number one, selling myself doesn't sound like something I want to do, and number two, I have no idea how to go about it. But here's an observation that I think is more useful than the idea that you have to sell yourself: the candidates that hiring committees like best are the ones who convey a sense of excitement about their work. This is an idea with which I am much more comfortable: of course I am excited about my work, or I wouldn't be doing it. And I want other people to be excited too. Moreover, if you have given a conference talk, you have already practiced this skill: the goal of a conference talk is to get the audience sufficiently excited that they might look at your paper.
Figuring out how to convey a sense of excitement is still hard, but there are things to be done:
Reconnect with whatever was interesting that led you to the work in the first place—especially the interesting problem.
Think about your best result and why you like it so much.
There are also some purely technical things (animal things, really) that make a difference when giving your job talk. Here's a time to apply all the usual advice given to public speakers and beginning teachers: don't hide behind a podium; don't stay tethered to your computer; walk among the audience and make eye contact; modulate the tone of your voice so that it varies in pitch and intensity. There are nonverbal ways to communicate to an audience what's background, what's scholarship, and especially "here comes one of the good bits." Use them.